Question: The equation of a circle $C$ is $x^2+y^2-18x-2y+57 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2-18x) + (y^2-2y) = -57$ $(x^2-18x+81) + (y^2-2y+1) = -57 + 81 + 1$ $(x-9)^{2} + (y-1)^{2} = 25 = 5^2$ Thus, $(h, k) = (9, 1)$ and $r = 5$.